%0 Journal Article
%J Computer Science Technical Reports
%D 1992
%T A Generalization of Brooks' Theorem
%A Srinivasan, Aravind
%X Given a connected graph $G = (V, E)$ with $n$ vertices and maximum degree $\Delta$ such that $\Delta \geq$ 3 and $G$ is not a complete graph, Brooks' theorem shows that $G$ is $\Delta$-colorable. We prove a generalization of this theorem: assume inductively that all but one vertex $v$ is colored; then, $v$ can be colored by considering the vertices (and their colors) in just an $O$ (log $n$) radius around $v$. Our proof uses a probabilistic technique to link the connectivity and diameter of "almost-regular" graphs, which could have other applications too.
%B Computer Science Technical Reports
%8 1992/09//
%G eng